Question

Find the area of the triangle. Round the answer to the nearest tenth.

A.
68.4 square units
B.
75.3 square units
C.
84.5 square units
D.
136.7 square units

Answer 1

The answer is A. 68.4 square units. If you need an explanation I can write it down.

Answer 2

Option A. 68.4 square units.

Explanation:

Since sides ED = EF = 13 units

So the given triangle is an isosceles triangle and in an isosceles triangle EFD, perpendicular drawn from E to DF, will be perpendicular bisector of DF.

Moreover, to this perpendicular bisector to DF will be the height of the triangle.

Now Area of a triangle of
`(1)/(2)` × base × height.

Sin 63 =
`(Height)/(Hypotenuse)` =
`(h)/(13)`

h = 13 sin 63 = 13 ( 0.891) = 11.583 units

Cos 63 =
`(Base)/(Hypotenuse)` =
`(Base)/(13)`

Base = 13 cos 63 = 13 × (0.454)

= 5.90 units

Since DF = 2 × base = 2 × 5.90

= 11.80 units

Now area of EDF =
`(1)/(2)` × 11.80 × 11.583

= 68.86 ≈ 68.40 square units.

Option A. 68.4 square units.